Stellar evolution with rotation XII. Pre-supernova models

We describe the latest developments of the Geneva stellar evolution code in order to model the pre-supernova evolution of rotating massive stars. Rotating and non-rotating stellar models at solar metallicity with masses equal to 12, 15, 20, 25, 40 and 60 Mwere computed from the ZAMS until the end of the core silicon burning phase. We took into account meridional circulation, secular shear instabilities, horizontal turbulence and dynamical shear instabilities. We find that dynamical shear instabilities mainly smoothen the sharp angular velocity gradients but do not transport angular momentum or chemical species over long distances. Most of the differences between the pre-supernova structures obtained from rotating and non-rotating stellar models have their origin in the effects of rotation during the core hydrogen and helium burning phases. The advanced stellar evolutionary stages appear too short in time to allow the rotational instabilities considered in this work to have a significant impact during the late stages. In particular, the internal angular momentum does not change significantly during the advanced stages of the evolution. We can therefore have a good estimate of the final angular momentum at the end of the core helium burning phase. The effects of rotation on pre-supernova models are significant between 15 and 30 M� . Indeed, rotation increases the core sizes (and the yields) by a factor ∼1.5. Above 20 M� , rotation may change the radius or colour of the supernova progenitors (blue instead of red supergiant) and the supernova type (IIb or Ib instead of II). Rotation affects the lower mass limits for radiative core carbon burning, for iron core collapse and for black hole formation. For Wolf-Rayet stars (M > 30 M� ), the pre-supernova structures are mostly affected by the intensities of the stellar winds and less by rotational mixing.